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A015305 Gaussian binomial coefficient [ n,5 ] for q = -2. 5
1, -21, 903, -25585, 875007, -27125217, 882215391, -28005209505, 899790907743, -28735427761313, 920460637644639, -29439916001972385, 942314556807454559, -30150270336284213409, 964869381941043396447, -30874848551033891160225 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

REFERENCES

J. Goldman and G.-C. Rota, The number of subspaces of a vector space, pp. 75-83 of W. T. Tutte, editor, Recent Progress in Combinatorics. Academic Press, NY, 1969.

I. P. Goulden and D. M. Jackson, Combinatorial Enumeration. Wiley, NY, 1983, p. 99.

M. Sved, Gaussians and binomials, Ars. Combinatoria, 17A (1984), 325-351.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 5..200

Index entries related to Gaussian binomial coefficients.

Index entries for linear recurrences with constant coefficients, signature (-21,462,3080,-14784,-21504,32768).

FORMULA

A015305(n) = T[n,5], where T is the triangular array A015109. - M. F. Hasler, Nov 04 2012

G.f.: x^5/((1-x)*(1+2*x)*(1-4*x)*(1+8*x)*(1-16*x)*(1+32*x)). - R. J. Mathar, Aug 03 2016

From G. C. Greubel, Sep 21 2019: (Start)

a(n) = (1 -11*(-2)^(n-4) +55*(-2)^(2*n-7) -55*(-2)^(3*n-9) +11*(-2)^(4*n- 10) -(-2)^(5*n-10))/40095.

E.g.f.: (11*exp(16*x) - 440 + 1024*exp(x) - 704*exp(-2*x) + 110*exp(-8*x) - exp(-32*x))/41057280. (End)

MAPLE

seq((1 -11*(-2)^(n-4) +55*(-2)^(2*n-7) -55*(-2)^(3*n-9) +11*(-2)^(4*n- 10) -(-2)^(5*n-10))/40095, n=5..25); # G. C. Greubel, Sep 21 2019

MATHEMATICA

Table[QBinomial[n, 5, -2], {n, 5, 20}] (* Vincenzo Librandi, Oct 29 2012 *)

PROG

(Sage) [gaussian_binomial(n, 5, -2) for n in range(5, 21)] # Zerinvary Lajos, May 27 2009

(PARI) a(n) = (1 -11*(-2)^(n-4) +55*(-2)^(2*n-7) -55*(-2)^(3*n-9) +11*(-2)^(4*n- 10) -(-2)^(5*n-10))/40095 \\ G. C. Greubel, Sep 21 2019

(MAGMA) [(1 -11*(-2)^(n-4) +55*(-2)^(2*n-7) -55*(-2)^(3*n-9) +11*(-2)^(4*n-10) -(-2)^(5*n-10))/40095: n in [5..25]]; // G. C. Greubel, Sep 21 2019

(GAP) List([5..25], n-> (1 -11*(-2)^(n-4) +55*(-2)^(2*n-7) -55*(-2)^(3*n-9) +11*(-2)^(4*n- 10) -(-2)^(5*n-10))/40095 ); # G. C. Greubel, Sep 21 2019

CROSSREFS

Diagonal k=5 of the triangular array A015109. See there for further references and programs. - M. F. Hasler, Nov 04 2012

Sequence in context: A041843 A041840 A012793 * A101732 A006301 A220384

Adjacent sequences:  A015302 A015303 A015304 * A015306 A015307 A015308

KEYWORD

sign,easy

AUTHOR

Olivier Gérard, Dec 11 1999

STATUS

approved

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Last modified July 9 09:40 EDT 2020. Contains 335542 sequences. (Running on oeis4.)